Method and apparatus for angular-resolved spectroscopic lithography characterization

ABSTRACT

An apparatus and method to determine a property of a substrate by measuring, in the pupil plane of a high numerical aperture lens, an angle-resolved spectrum as a result of radiation being reflected off the substrate. The property may be angle and wavelength dependent and may include the intensity of TM- and TE-polarized radiation and their relative phase difference.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Divisional of U.S. patent application Ser. No.16/270,155, filed Feb. 7, 2019, which is a Divisional of U.S. patentapplication Ser. No. 14/264,547, filed Apr. 29, 2014, which is aContinuation of U.S. patent application Ser. No. 14/011,663, filed Aug.27, 2013, which is a Divisional of U.S. patent application Ser. No.13/249,566, filed Sep. 30, 2011, which is a Continuation of U.S. patentapplication Ser. No. 12/805,852, filed Aug. 20, 2010 which is aContinuation of U.S. patent application Ser. No. 11/203,418, filed Aug.15, 2005, which is a Continuation-in-Part of U.S. patent applicationSer. No. 10/918,742, filed Aug. 16, 2004, which are all incorporated byreference herein in their entireties.

BACKGROUND OF THE INVENTION Field of the Invention

The present invention relates to methods of inspection usable, forexample, in the manufacture of devices by lithographic techniques and tomethods of manufacturing devices using lithographic techniques.

Background Art

In a manufacturing process using a lithographic projection apparatus, apattern (e.g. in a mask) is imaged onto a substrate that is at leastpartially covered by a layer of radiation-sensitive material (resist) bythe changes of either optical properties or surface physical propertiesof the resist. Alternatively, the imaging step may use a resistlessprocess such as etched grating or nano-imprint technology. Prior to thisimaging step, the substrate may undergo various procedures, such aspriming, resist coating and a soft bake. After exposure, the substratemay be subjected to other procedures, such as a post-exposure bake(PEB), development, a hard bake and measurement/inspection of the imagedfeatures. This array of procedures is used as a basis to pattern anindividual layer of a device, e.g. an IC. Such a patterned layer maythen undergo various processes such as etching, ion-implantation(doping), metallization, oxidation, chemical-mechanical polishing, etc.,all intended to finish off an individual layer. If several layers arerequired, then the whole procedure, or a variant thereof, will have tobe repeated for each new layer. Eventually, an array of devices will bepresent on the substrate (wafer). These devices are then separated fromone another by a technique such as dicing or sawing, whence theindividual devices can be mounted on a carrier, connected to pins, etc.

The measurement and inspection step after development of the resist (orsubstrate surface in the case of etching), referred to as in-linebecause it is carried out in the normal course of processing productionsubstrates, typically serves two purposes. Firstly, it is desirable todetect any target areas where the pattern in the developed resist isfaulty. If a sufficient number of target areas are faulty, the substratecan be stripped of the patterned resist and re-exposed, hopefullycorrectly, rather than making the fault permanent by carrying out aprocess step, e.g., an etch, with a faulty pattern. Secondly, themeasurements may allow errors in the lithographic apparatus, e.g.illumination settings or exposure dose, to be detected and corrected forin subsequent exposures. However, many errors in the lithographicapparatus cannot easily be detected or quantified from the patternsprinted in resist. Detection of a fault does not always lead directly toits cause. Thus, a variety of off-line procedures for detecting andmeasuring errors in the lithographic apparatus are known. These mayinvolve replacing the substrate with a measuring device or carrying outexposures of special test patterns, e.g., at a variety of differentmachine settings. Such off-line techniques take time, often aconsiderable amount, during which the end products of the apparatus willbe of an unknown quality until the measurement results are madeavailable. Therefore, in-line techniques, ones which can be carried outat the same time as production exposures, for detecting and measuringerrors in the lithographic apparatus, are usually preferred.

Scatterometry is one example of an optical metrology technique that canbe used for in-line measurements of CD and overlay. There are two mainscatterometry techniques:

-   -   (1) Spectroscopic scatterometry measures the properties of        scattered light at a fixed angle as a function of wavelength,        usually using a broadband light source such as xenon, deuterium,        or halogen based light source such as a xenon arc lamp. The        fixed angle can be normally incident or obliquely incident.    -   (2) Angle-resolved scatterometry measures the properties of        scattered light at a fixed wavelength as a function of angle of        incidence, usually using a laser as a single wavelength light        source.

The structure giving rise to a reflected spectrum is reconstructed,e.g., using real-time regression or by comparison to a library ofpatterns derived by simulation. Reconstruction involves minimization ofa cost function. Both approaches calculate the scattering of light byperiodic structures. The most common technique is Rigorous Coupled-WaveAnalysis (RCWA), though light scattering can also be calculated by othertechniques such as Finite Difference Time Domain (FDTD) or IntegralEquation techniques.

A problem with known angle-resolved scatterometry techniques is thatthey only detect one wavelength at a time so spectra with more than onewavelength have to have those wavelengths time-multiplexed, whichincreases the total acquisition time taken to detect and process thespectra. In spectroscopic scatterometry, an extended light source with alarge etendue is used. Since a small grating must be illuminated with asmall spread in angle of incidence, a lot of light from this extendedsource is wasted. This results in low light levels on the detector thatlead to long acquisition times, which have a negative impact onthroughput. If short acquisition times are chosen, the measurementresults might not be stable.

BRIEF SUMMARY OF THE INVENTION

Accordingly, it would be advantageous, for example, to provide a methodof measuring overlay and grating shape parameters (such as gratingasymmetry and alignment) during manufacture of devices usinglithographic techniques and measurement of an angle-resolved spectrum ina pupil plane (or back focal plane) of a high NA (numerical aperture)lens. Projection system aberrations, etc. can also be measured in orderto be corrected or compensated for.

Embodiments of the present invention may encompass hardware that iscapable of measuring angle-resolved spectra at multiple wavelengthssimultaneously, of carrying out immersion scatterometry and a focusmeasurement method for an angle-resolved scatterometer, and of measuringintensity noise of a radiation source with a 2-D detector array.Furthermore, embodiments of the present invention may encompassapplications of the hardware including measuring overlay through themeasurement of asymmetry of scattered light and measuring small lineshape variations via Rayleigh anomalies and high diffraction orders ofscattered light.

Although specific reference may be made in this text to the use of theapparatus according to the invention in the manufacture of ICs, itshould be explicitly understood that such an apparatus has many otherpossible applications. For example, it may be employed in themanufacture of integrated optical systems, guidance and detectionpatterns for magnetic domain memories, liquid-crystal display panels,thin-film magnetic heads, etc. The skilled artisan will appreciate that,in the context of such alternative applications, any use of the terms“reticle”, “wafer” or “die” in this text should be considered as beingreplaced by the more general terms “mask”, “substrate” and “targetportion”, respectively.

In the present document, the terms “radiation” and “beam” are used toencompass all types of electromagnetic radiation, including ultravioletradiation (e.g. with a wavelength of 365, 248, 193, 157 or 126 nm) andEUV (extreme ultra-violet radiation, e.g., having a wavelength in therange 5-20 nm), as well as particle beams, such as ion beams or electronbeams.

BRIEF DESCRIPTION OF THE DRAWINGS/FIGURES

Embodiments of the invention will now be described, by way of exampleonly, with reference to the accompanying schematic drawings in whichcorresponding reference symbols indicate corresponding parts and inwhich:

FIG. 1 depicts a lithographic projection apparatus that may be used toperform a method according to an embodiment of the invention;

FIG. 2 depicts a scatterometer;

FIG. 3 depicts the general operating principle of measuring anangle-resolved spectrum in the pupil plane of a high NA lens accordingto an embodiment of the invention;

FIGS. 4 a and 4 b depict the use of an embodiment of the presentinvention in determining overlay;

FIG. 5 depict the use of a non-polarizing beam splitter for coupling offa portion of a radiation beam according to an embodiment of theinvention;

FIG. 6 depicts a wavelength multiplexer according to an embodiment ofthe invention;

FIG. 7 depicts a wavelength demultiplexer according to an embodiment ofthe invention;

FIG. 8 depicts a knife edge at an intermediate object plane according toan embodiment of the invention;

FIGS. 9 a and 9 b depict a shaped obscuration in an inspection beamaccording to an embodiment of the invention;

FIG. 10 depicts a detected image of different diffraction orders ofscattered spectra according to an embodiment of the invention;

FIG. 11 depicts a scatterometer with two illumination spots according toan embodiment of the invention;

FIG. 12 depicts an ellipsometer according to an embodiment of thepresent invention;

FIG. 13 depicts a scatterometer configured to detect images in the pupilplane and the image plane according to an embodiment of the presentinvention; and

FIG. 14 depicts a grating overlay of twice the pitch of a grating.

FIGS. 15A-15C show a concave mirror, a convex mirror, and a plurality ofplane mirrors tilted at different angles, according to variousembodiments of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 schematically depicts a lithographic projection apparatus useablein a method according to an embodiment of the invention. The apparatuscomprises:

-   -   a radiation system Ex, IL, for supplying a projection beam PB of        radiation (e.g. DUV radiation), which in this particular case        also comprises a radiation source LA;    -   a first object table (mask table) MT provided with a mask holder        for holding a mask MA (e.g. a reticle), and connected to a first        positioning device for accurately positioning the mask with        respect to item PL;    -   a second object table (substrate table) WT provided with a        substrate holder for holding a substrate W (e.g. a resist-coated        silicon wafer), and connected to a second positioning device for        accurately positioning the substrate with respect to item PL;    -   a projection system (“projection lens”) PL (e.g. a refractive        lens system) for imaging an irradiated portion of the mask MA        onto a target portion C (e.g. comprising one or more dies) of        the substrate W.

As here depicted, the apparatus is of a transmissive type (e.g. has atransmissive mask). However, in general, it may also be of a reflectivetype, for example (e.g. with a reflective mask). Alternatively, theapparatus may employ another kind of patterning device, such as aprogrammable mirror array of a type as referred to above.

The source LA (e.g. an excimer laser) produces a beam of radiation. Thisbeam is fed into an illumination system (illuminator) IL, eitherdirectly or after having traversed conditioning means, such as a beamexpander Ex, for example. The illuminator IL may comprise adjustingmeans AM for setting the outer and/or inner radial extent (commonlyreferred to as σ-outer and σ-inner, respectively) of the intensitydistribution in the beam. In addition, it will generally comprisevarious other components, such as an integrator IN and a condenser CO.In this way, the beam PB impinging on the mask MA has a desireduniformity and intensity distribution in its cross-section.

It should be noted with regard to FIG. 1 that the source LA may bewithin the housing of the lithographic projection apparatus (as is oftenthe case when the source LA is a mercury lamp, for example), but that itmay also be remote from the lithographic projection apparatus, theradiation beam which it produces being led into the apparatus (e.g. withthe aid of suitable directing mirrors); this latter scenario is oftenthe case when the source LA is an excimer laser. The current inventionand claims encompass both of these scenarios.

The beam PB subsequently intercepts the mask MA, which is held on a masktable MT. Having traversed the mask MA, the beam PB passes through theprojection lens PL, which focuses the beam PB onto a target portion C ofthe substrate W. With the aid of the second positioning device (and aninterferometric measuring device IF), the substrate table WT can bemoved accurately, e.g. so as to position different target portions C inthe path of the beam PB. Similarly, the first positioning device can beused to position the mask MA accurately with respect to the path of thebeam PB, e.g. after mechanical retrieval of the mask MA from a masklibrary, or during a scan. In general, movement of the object tables MT,WT will be realized with the aid of a long-stroke module (coarsepositioning) and a short-stroke module (fine positioning), which are notexplicitly depicted in FIG. 1 . However, in the case of a stepper (asopposed to a step-and-scan apparatus) the mask table MT may just beconnected to a short stroke actuator, or may be fixed.

The depicted apparatus can be used in two different modes:

1. In step mode, the mask table MT is kept essentially stationary, andan entire mask image is projected at one time (i.e. a single “flash”)onto a target portion C. The substrate table WT is then shifted in the Xand/or Y directions so that a different target portion C can beirradiated by the beam PB;

2. In scan mode, essentially the same scenario applies, except that agiven target portion C is not exposed in a single “flash”. Instead, themask table MT is movable in a given direction (the so-called “scandirection”, e.g. the Y direction) with a speed v, so that the projectionbeam PB is caused to scan over a mask image; concurrently, the substratetable WT is simultaneously moved in the same or opposite direction at aspeed V=Mv, in which M is the magnification of the projection system PL(typically, M=¼ or ⅕). In this manner, a relatively large target portionC can be exposed, without having to compromise on resolution.

One or more properties of the surface of a substrate 6 may be determinedusing a scatterometer such as that depicted in FIG. 2 . In anembodiment, the scatterometer comprises a broadband (white light)radiation source 2, which directs radiation onto a substrate 6. Anextended broadband radiation source may be configured to provide theradiation beam with a wavelength of at least 50 nm to the substratesurface. The reflected radiation is passed to a spectrometer detector 4,which measures a spectrum 10 (intensity as a function of wavelength) ofthe specular reflected radiation. From this data, the structure orprofile giving rise to the detected spectrum may be reconstructed, e.g.by Rigorous Coupled Wave Analysis and non-linear regression or bycomparison with a library of simulated spectra as shown at the bottom ofFIG. 2 . In general, for the reconstruction, the general form of thestructure is known and some parameters are assumed from knowledge of theprocess by which the structure was made, leaving only a few parametersof the structure to be determined from the scatterometry data.

The scatterometer may be a normal-incidence scatterometer or anoblique-incidence scatterometer. Variants of scatterometry may also beused in which the reflection is measured at a range of angles of asingle wavelength, rather than the reflection at a single angle of arange of wavelengths.

In one or more embodiments described below, there is used ascatterometer configured to measuring a property of a substrate bymeasuring, in a pupil plane 40 of a high NA lens, a property of anangle-resolved spectrum reflected from the substrate surface 6 at aplurality of angles and wavelengths as shown in FIG. 3 . Thescatterometer comprises a radiation source 2 configured to projectradiation onto the substrate and a detector 32 configured to detect thereflected spectra. The pupil plane is the plane in which the radialposition of radiation defines the angle of incidence and the angularposition defines the azimuth angle of the radiation and anysubstantially conjugate plane. The detector 32 is placed in the pupilplane of the high NA lens. The NA is high and, in an embodiment, atleast 0.9 or at least 0.95. Immersion scatterometers may even havelenses with a NA over 1.

Previous angle-resolved scatterometers have only measured the intensityof scattered radiation. An embodiment of the present invention allowsseveral wavelengths to be measured simultaneously at a range of angles.The properties measured by the scatterometer for different wavelengthsand angles may include the intensity of transverse magnetic (TM) andtransverse electric (TE) polarized radiation and the phase differencebetween the TM and TE polarized radiation.

Using a broadband light source (i.e. one with a wide range of lightfrequencies or wavelengths—and therefore of colors) is possible, whichgives a large etendue, allowing the mixing of multiple wavelengths. Theplurality of wavelengths in the broadband light, in an embodiment, eachhas a bandwidth of, say, δλ and a spacing, therefore, of at least 2 δλ(i.e. twice the wavelength). Several “sources” of radiation can bedifferent portions of an extended radiation source that have been splitusing, say, fiber bundles. In this way, angle-resolved scatter spectracan be measured at multiple wavelengths in parallel. A 3-D spectrum(wavelength and two different angles) may be measured, which containsmore information than a 2-D spectrum. This allows more information to bemeasured which increases metrology process robustness.

A scatterometer of an embodiment of the present invention is shown inFIG. 3 . The light source 2 is focused using lens system L2 throughinterference filter 30 and is focused onto substrate 6 via a microscopeobjective lens L1. The radiation is then reflected via partiallyreflective surface 34 into a CCD detector in the back projected pupilplane 40 in order to have the scatter spectrum detected. The pupil plane40 is at the focal length of the lens system L1. A detector and high NAlens are placed at the pupil plane. The pupil plane may be re-imagedwith auxiliary optics since the pupil plane of a high NA lens is usuallylocated inside the lens.

The pupil plane of the reflector light is imaged on the CCD detectorwith an integration time of, for example, 40 milliseconds per frame. Inthis way, a two-dimensional angular scatter spectrum of the substratetarget is imaged on the detector. The detector may be, for example, anarray of CCD detectors or CMOS detectors. The processing of the spectrumgives a symmetrical detection configuration and so sensors can be maderotationally symmetrical. This allows the use of a compact substratetable because a target on the substrate can be measured at anyrotational orientation relative to the sensor. All the targets on thesubstrate can be measured by a combination of a translation and arotation of the substrate.

A set of interference filters 30 may be available to select a wavelengthof interest in the range of, say, 405-790 nm or even lower, such as200-300 nm. The interference filter may be tunable rather thancomprising a set of different filters. A grating could be used insteadof one or more interference filters.

The substrate 6 (or even the reflective surface 34) may be a grating.The grating may be printed such that after development, a series of barsare formed of solid resist lines. The bars may alternatively be etchedinto the substrate. This pattern is sensitive to comatic aberrations ina lithographic projection apparatus, particularly the projection systemPL, and illumination symmetry and the presence of such aberrations willmanifest themselves in a variation in the printed grating. Accordingly,the scatterometry data of the printed gratings is used to reconstructthe gratings. One or more parameters of the grating, such as line widthsand shapes, may be input to the reconstruction process from knowledge ofthe printing step and/or other scatterometry processes.

In transmission metallic gratings with rectangular slits, complexphotonic band structures (CPBS) are shown to exhibit strongdiscontinuities, which are located on Wood-Rayleigh anomalies and revealtwo types of resonance, which are referred to as horizontal and verticalsurface-plasmon resonances. Spectral position and width of peaks in thespectrum can be directly extracted from CPBS for both horizontal andvertical resonances. In this way, the radiation coming off atransmission metallic grating can have its spectrum analyzed and one ormore properties of the grating determined by the strong discontinuitieslocated on the Wood-Rayleigh anomalies. Wood-Rayleigh anomalies occurupon the variation of wavelength or angle of incidence, giving anadditional propagating diffraction order. The greater the beam width,the greater the lateral displacement of the beam.

An embodiment of the present invention detects the spectrum and createsa symmetrical pupil plane image from which the discontinuities can bemeasured and one or more grating properties therefore calculated.

According to an embodiment of the invention, the scatterometer may beadapted to measure the overlay of two misaligned periodic structures bymeasuring asymmetry in the reflected spectrum, the asymmetry beingrelated to the extent of the overlay.

In an embodiment, the scatterometer is adapted to measure the overlay oftwo misaligned gratings or periodic structures by measuring asymmetry inthe reflected spectrum and/or the detection configuration, the asymmetrybeing related to the extent of the overlay. Thanks to the symmetricaldetection configuration, any asymmetry is clearly distinguishable. Thisprovides a straightforward way to measure misalignment in the gratings.

One type of substrate pattern used is shown in FIG. 4 . A grating 14 hasa second grating 12 printed on top of it. The amount by which thegrating 12 is offset with respect to grating 14 is known as the overlay22.

Note that in the embodiment shown in FIG. 4 a , the radiation source 2illuminates the object symmetrically with respect to the surface normaland the scatterometry detector measures scatter radiation from severalangles, although a source which illuminates the object from an obliqueangle is also possible.

Overlay metrology is based on the measurement of an asymmetry in theangular scatter spectrum. Symmetric structures yield symmetric angularspectra and an asymmetry in the target shows up as an asymmetry in theangular scatter spectrum. This property is the basis of overlaymetrology using angle-resolved scatterometry.

Two overlapping but misaligned gratings 12 and 14 made of bars withwidth 20 form one composite asymmetric target. The resulting asymmetryin the angular scatter spectrum is detected with the angle-resolvedscatterometer 4 shown in FIG. 3 and used to derive the overlay 22 in thefollowing manner:

Two grating pairs are used with a deliberate bias of +d and −d in,respectively, the first and second pair. In other words, grating 12 isshifted in one direction in one pair (as shown in FIG. 4 ) and in theopposite direction in the other pair (not shown). The actual transverseshift between the gratings in each pair is therefore X1=OV+d andX2=OV−d, OV being the overlay 22.

When the grating pairs are aligned, the overlay is 0 and if theintensity of the illumination incident on the gratings is Iill and theintensity of the radiation reflected off the gratings is I+1 in a firstdirection and I−1 in the opposite direction but in the same plane, whenthe overlay, OV=0,I ₊₁ =I ⁻¹.  (1)

However, ifOV≠0,I ₊₁ ≠I ⁻¹.  (2)

For a small overlay, the intensity difference is proportional to theoverlay:I ₊₁ −I ⁻¹ =K×OV.  (3)K is a constant and is process dependent and therefore unknown.

In order to calibrate the overlay metrology with the scatterometeraccording to an embodiment of the present invention, two grating targetsare used; one with the overlay shown in FIG. 4 b and a second with theexact reverse overlay, so the upper grating 12 is displaced to the leftrather than the right with respect to the bottom grating 14. The overlayin the first set-up is OV+d (distance 22 in FIG. 4 b ) and the overlayin the second set-up is OV−d.

So, forOV+d,asymmetryA ₊ =K(OV+d)  (4)and forOV−d,asymmetryA ⁻ =K(OV−d).  (5)

The scaling factor K can be eliminated:

$\begin{matrix}{{OV} = {d\frac{A_{+} + A_{-}}{A_{+} - A_{-}}}} & (6)\end{matrix}$

The overlay can therefore be calculated using measurements of theasymmetry in the angle-resolved scatter spectrum.

An advantage of this method compared to previously known methods is thefact that only two gratings are required. Moreover, in principle, themethod can also work for 2-D gratings: in that case only 2 gratings arerequired for a complete (x,y) overlay measurement. This is a significantimprovement compared to, say, 6 gratings that spectroscopicscatterometry methods use.

The analysis of xy overlay metrology using 2-D gratings is as follows:

Two gratings have an amplitude transmission of f(x,y) and g(x,y). Thesegratings are periodic in two directions and their transmissions cantherefore be written as a Fourier series:

$\begin{matrix}{{{f\left( {x,y} \right)} = {\sum\limits_{n}{\sum\limits_{m}{F_{n,m}e^{- {j({{nx} + {my}})}}}}}}{{g\left( {x,y} \right)} = {\sum\limits_{p}{\sum\limits_{q}{G_{p,q}e^{- {j({{px} + {qy}})}}}}}}} & (7)\end{matrix}$

Both gratings have an equal period and for simplicity the periods of thegratings have been normalized to 2π for the following calculations. Thecoefficients F_(n,m) and G_(p,q) can be interpreted as diffractionefficiencies that depend on the grating shape, wavelength andpolarization. The two gratings overlap with a relative overlay of x0 andy0 in, respectively, the x and y directions. The total transmission tcan be written as:

$\begin{matrix}\begin{matrix}{{t\left( {x,y} \right)} = {{f\left( {x,y} \right)}{g\left( {{x - x_{0}},{y - y_{0}}} \right)}}} \\{= {\sum\limits_{n}{\sum\limits_{m}{\sum\limits_{p}{\sum\limits_{q}{F_{n,m}G_{p,q}^{\prime}e^{- {j({{{({p + n})}x} + {{({q + m})}y}})}}}}}}}}\end{matrix} & (8)\end{matrix}$ $\begin{matrix}{{{where}:G_{p,q}^{\prime}} = {G_{p,q}e^{j({{px_{0}} + {qy}_{0}})}}} & (9)\end{matrix}$

The variables can be adjusted as follows:p+n=a⇒p=a−nq+m=b⇒q=b−m

Substituting these expressions in the Fourier series of t(x,y) yields:

$\begin{matrix}\begin{matrix}{{t\left( {x,y} \right)} = {\sum\limits_{n}{\sum\limits_{m}{\sum\limits_{p}{\sum\limits_{q}{F_{n,m}G_{n,m}^{\prime}e^{- {j({{{({p + n})}x} + {{({q + m})}y}})}}}}}}}} \\{= {\sum\limits_{a}{\sum\limits_{b}{T_{a,b}e^{- {j({{ax} + {by}})}}}}}}\end{matrix} & (10)\end{matrix}$ $\begin{matrix}{{{where}:T_{a,b}} = {\sum\limits_{n}{\sum\limits_{m}{F_{n,m}G_{{a - n},{b - m}}^{\prime}}}}} & (11)\end{matrix}$T_(a,b) can be interpreted as the amplitude of the diffraction order(a,b). It can be see that this amplitude generally depends on theoverlay in the x and y direction.

For simplicity, only diffraction orders running in the x-direction areconsidered. The analysis that follows can also be done for diffractionorders in the y-direction. This would only require an adjustment ofvariables.

For diffraction orders that run in the x-direction, b=0, so for theamplitude of two diffraction orders a and −a:

$\begin{matrix}{{T_{a,0} = {\sum\limits_{n}{\sum\limits_{m}{F_{n,m}G_{{a - n},{- m}}e^{j({{{({a - n})}x_{0}} - {my}_{0}})}}}}}{T_{{- a},0} = {\sum\limits_{n}{\sum\limits_{m}{F_{n,m}G_{{{- a} - n},{- m}}e^{j({{{({{- a} - n})}x_{0}} - {my}_{0}})}}}}}} & (12)\end{matrix}$taking the factor e^(±jax) ⁰ in front of the summation yields:

$\begin{matrix}{{T_{a,0} = {e^{{jax}_{0}}{\sum\limits_{n}{\sum\limits_{m}{F_{n,m}G_{{a - n},{- m}}e^{- {j({{nx}_{0} + {my}_{0}})}}}}}}}\begin{matrix}{T_{{- a},0} = {e^{- {jax}_{0}}{\sum\limits_{n}{\sum\limits_{m}{F_{n,m}G_{{{- a} - n},{- m}}e^{- {j({{nx}_{0} - {my}_{0}})}}}}}}} \\{e^{- {jax}_{0}}{\sum\limits_{- n}{\sum\limits_{m}{F_{{- n},m}G_{{{- a} + n},{- m}}e^{j({{nx}_{0} - {my}_{0}})}}}}}\end{matrix}} & (13)\end{matrix}$

Assuming that both gratings are symmetric in the x-direction:F _(−n,m) =F _(n,m)G _(−n,m) =G _(n,m)  (14)

Using this property yields for the diffracted amplitudes:

$\begin{matrix}{{T_{a,0} = {e^{{jax}_{0}}{\sum\limits_{n}{\sum\limits_{m}{F_{n,m}G_{{a - n},{- m}}e^{- {j({{nx}_{0} + {my}_{0}})}}}}}}}{T_{{- a},0} = {e^{- {jax}_{0}}{\sum\limits_{n}{\sum\limits_{m}{F_{n,m}G_{{a - n},{- m}}e^{j({{nx}_{0} - {my}_{0}})}}}}}}} & (15)\end{matrix}$

The scatterometer measures the intensities of the diffracted fields,giving:I _(±a,0) =|T _(±a,0)═²  (16)

Evaluation of this expression shows that the intensity can be written inthe form:

$\begin{matrix}{{I_{a,0} = {\sum\limits_{n}{\sum\limits_{m}{B_{n,m}{\cos\left( {\varepsilon_{n,m} - {nx_{0}} - {my_{0}}} \right)}}}}}{I_{{- a},0} = {\sum\limits_{n}{\sum\limits_{m}{B_{n,m}{\cos\left( {\varepsilon_{n,m} + {nx_{0}} - {my_{0}}} \right)}}}}}} & (17)\end{matrix}$where the amplitudes B_(n,m) and phases ε_(n,m) depend on the gratingshapes, illumination wavelength and illumination polarization. Takingthe difference of the +1 and −1 order yields an asymmetry A_(x) thatruns in the x-direction:

$\begin{matrix}\begin{matrix}{A_{x} = {I_{1,0} - I_{{- 1},0}}} \\{{\sum\limits_{n}{\sum\limits_{m}{B_{n,m}{\cos\left( {\varepsilon_{n,m} - {nx_{0}} - {my_{0}}} \right)}}}} -} \\{\sum\limits_{n}{\sum\limits_{m}{B_{n,m}{\cos\left( {\varepsilon_{n,m} + {nx_{0}} - {my_{0}}} \right)}}}} \\{\sum\limits_{n}{\sum\limits_{m}{2B_{n,m}{\sin\left( {\varepsilon_{n,m} - {my_{0}}} \right)}{\sin\left( {nx_{0}} \right)}}}}\end{matrix} & (18)\end{matrix}$

In practice the overlay is small compared to the pitch of the gratings.For example, the pitch is often of the order of 1 μm and the maximumoverlay is of the order of 60 nm. The expression above can therefore belinearized and only the linear terms in x₀ and y₀ retained:

$\begin{matrix}\begin{matrix}{A_{x} = {\sum\limits_{n}{\sum\limits_{m}{2B_{n,m}{\sin\left( {\varepsilon_{n,m} - {my_{0}}} \right)}{\sin\left( {nx_{0}} \right)}}}}} \\{= {\sum\limits_{n}{\sum\limits_{m}{2{B_{n,m}\left\lbrack {{{\sin\left( \varepsilon_{n,m} \right)}{\cos\left( {my_{0}} \right)}} - {{\cos\left( \varepsilon_{n,m} \right)}{\sin\left( {my_{0}} \right)}}} \right\rbrack}{\sin\left( {nx_{0}} \right)}}}}} \\{\cong {\sum\limits_{n}{\sum\limits_{m}{2{B_{n,m}\left\lbrack {{\sin\left( \varepsilon_{n,m} \right)} - {\cos\left( \varepsilon_{n,m} \right)}} \right\rbrack}{nx}_{0}}}}} \\{= {{x_{0}K_{0}} + {K_{xy}x_{0}y_{0}}}}\end{matrix} & (19)\end{matrix}$ $\begin{matrix}{{{{where}K_{0}} = {\sum\limits_{n}{\sum\limits_{m}{2nB_{n,m}{\sin\left( \varepsilon_{n,m} \right)}}}}}{K_{xy} = {\sum\limits_{n}{\sum\limits_{m}{2mnB_{n,m}{\cos\left( \varepsilon_{n,m} \right)}}}}}} & (20)\end{matrix}$

It can be seen that there is a coupling term: The asymmetry in thex-direction is also a function of the y-overlay via the coupling termK_(xy). If the 2-D grating has 90° rotation symmetry and if the light ispolarized at 45°, then we can write for the asymmetry in the x and ydirections:A _(x) =x ₀ K ₀ +K _(xy) x ₀ y ₀A _(y) =y ₀ K ₀ +K _(xy) x ₀ y ₀  (21)

These equations are the basis for xy overlay metrology with two 2-Dgrating pairs. In the first grating pair, a bias of +d is introduced inthe upper grating and in the second grating pair, a bias of −d isintroduced. This bias is applied in both the x and y direction. Fourasymmetry terms can now be measured: An x and y asymmetry in the firstgrating pair and an x and y asymmetry in the second grating pair areshown as:A _(1x) =K ₀(OV _(x) +d)+K _(xy)(OV _(y) +d)(OV _(x) +d)A _(1y) =K ₀(OV _(y) +d)+K _(xy)(OV _(y) +d)(OV _(x) +d)A _(2x) =K ₀(OV _(x) −d)+K _(xy)(OV _(y) −d)(OV _(x) +d)A _(2y) =K ₀(OV _(y) −d)±K _(xy)(OV _(y) −d)(OV _(x) −d)  (22)

This gives four non-linear equations with four unknowns K0, Kxy, OVx andOVy which can be solved to give the overlay.

In an embodiment, one or more apertures may be provided to thescatterometer to mimic lithography exposure conditions when the gratingpattern(s) was created. The apertures may then be used in the creationof the angle-resolved spectroscopic image of the grating pattern(s)using the scatterometer.

In an embodiment, it is possible to immerse at least part of the spacebetween the substrate and the detector in liquid, more specifically, thespace between lens L1 and the substrate 6 as shown in FIG. 3 . Theliquid may be water. This has an advantage of increasing the spatialbandwidth of the medium between the substrate 6 and the lens L1. Thismeans that a diffraction that would be evanescent, for example, in aircan propagate and be captured by the lens. With immersion of the space,therefore, it becomes possible to detect a higher diffraction order thatcontains more detailed information about the grating under investigationthan with, for example, air in the space. In an embodiment, thenumerical aperture (NA) of the scatterometer is at least 0.9, even 0.95or above 1.

Immersing the space between L1 and the object with a high refractiveindex fluid increases the spatial bandwidth of the medium and allows thepropagation of a higher diffraction order for smaller pitches. Thesmallest pitch that creates a propagating first order spectrum is

$\frac{\lambda}{\left( {2NA} \right)}.$Assuming NA equals 1.3 and λ equals 400 nm, this yields a minimum pitchof 154 nm. This corresponds to a critical dimension (CD) orreconstructed grating width of approximately 20 to 80 nm. When lookingat a profile such as that shown in FIG. 2 , the critical dimension isthe mean width of a peak and the pitch is the distance from one peak tothe next.

The immersion fluid should have a large index step with respect to, forexample, the resist that is on the substrate 6. This may allow maximumcontrast in the detector image. A possible liquid that fulfils suchrequirements is water.

FIG. 5 shows, according to an embodiment of the invention, the use ofone and the same detector to monitor the source output intensity and theintensity of scattered radiation, which avoids synchronization problemsand allows a real-time compensation for source output variations.

The scatterometer may comprise a non-polarizing beam splitter and atilted mirror for coupling off a portion of the radiation beam emittedfrom the radiation source for separate measurement with the samedetector. In an embodiment, the portion of the radiation beam is used tomeasure the intensity of the radiation beam and the scatterometer may beadapted to compensate for fluctuations in intensity of the radiationbeam. Advantages of using the same CCD detector for the intensitymeasurement beam alongside the main measurement beam are that no extradetector is required and so there is no difference in optical andthermal properties between a reference sensor and a metrology sensor;and there are no extra electronics required to trigger, read out andstore the reference signal. Any intensity variations may be measured andcompensated for.

A non-polarizing beam splitter 50 in the radiation path images scatteredradiation on a two-dimensional detector 32. An extra lens re-images thepupil plane onto the CCD detector. The intensity incident on thedetector is shown as image 36. The non-polarizing beam splitter 50 alsocouples out a portion of the radiation beam to use it for monitoringintensity noise. Instead of measuring this radiation portion with aseparate detector, the radiation is retro-reflected using tilted mirror52 and transmitted to a separate part of the same detector 32. Tiltedmirror 52 can be titled by an actuator 51. Further, although a planetilted mirror 52 is shown, a concave mirror 52 a, a convex mirror 52 b,or a plurality of plane mirrors 52 c tilted at different angles, canalternatively be used, as shown in FIGS. 15A-C, respectively. Anoptional pupil stop 54 limits the extent of the radiation portion andthe mirror tilt ensures that the radiation portion is projectedalongside the main radiation beam. The spectrum is imaged onto thedetector 32 at the pupil plane of L1.

In previous methods, angle-resolved scatterometry has been done at asingle wavelength. Measurements at different wavelengths would then havebeen done sequentially and the different wavelengths would be timemultiplexed. However, time multiplexing of the wavelengths may degradethroughput.

In an embodiment, the scatterometer comprises a wavelength multiplexerbetween the radiation source and the substrate and a demultiplexerbetween the substrate and the detector. This allows several differentwavelengths (or colors) to be measured simultaneously, giving moreinformation in a shorter time frame and therefore robustness asdiscussed above.

In an embodiment, the surface area of the radiation source is split intoN parts that are each coupled to a wavelength multiplexer, where N isthe number of discrete wavelengths. This splitting can be done, forexample, with fiber bundles and the like.

In an embodiment, the wavelength multiplexer comprises a dispersiveelement placed at a back-projected object plane. The dispersive elementmay be a grating or prism adapted to accommodate N discrete wavelengthseach with a bandwidth δλ and a spacing of at least twice the bandwidth,i.e. 2 δλ. This may maximize the usage of an extended light source.Measurement of different wavelengths no longer has to betime-multiplexed because it can be done at the same time, and so a majoradvantage is that throughput is increased. The wavelength multiplexermay, alternatively or additionally, comprise a dispersive element placedat a pupil plane.

In an embodiment, the demultiplexer comprises a dispersive elementplaced at a pupil plane. One or more optical wedges may be inserted inthe object plane to achieve well-defined separation of angle-resolvedspectra in the pupil plane.

In an embodiment, an extended broadband radiation source such as axenon, deuterium or quartz tungsten halogen light source is used. Thesesources have a large etendue that gives a surface area that can be splitinto discrete wavelengths and offer more information as discussed above.The wavelengths may be in the range of 193 to 800 nm.

In an embodiment, a dispersive prism or grating which combines Ndiscrete wavelengths is used in the illumination branch (or theradiation path between the source 2 and the substrate 6 in FIG. 2 ) anda grating or prism is used in the detection branch (or the space betweenthe radiation path between the substrate 6 and the detector 4) tospatially separate the wavelengths.

An example of a multiplexing grating is shown in FIG. 6 . Two lightsources S1 and S2 are transmitted through a lens system L2 and strike aLittrow mounted grating 16 which is in the object plane 42 and arefocused on the pupil plane 40 before being transmitted through a lenssystem L1 to another object plane 42 and optionally into an illuminationfiber 60. The pupil plane contains rectangular apertures of suitabledimensions—the width determining the angular extent of the lightincident on the grating. This angular extent and the grating pitchdetermine the bandwidth of the returning light that is transmitted viathe aperture in the pupil plane. For example, a grating with 1200 linesper millimeter yields a dispersion of approximately 1.2 mrad/nm. Aneffective bandwidth of 4 nm corresponds to a full angular width of theillumination beam of 3.33 mrad. The spot size of the substrate 6 isapproximately 40 μm and its NA is 0.95. The beam diameter on the gratingis therefore approximately 23 mm. If the focal length of the lens L1 is100 mm, then the width of the aperture holes in the pupil plane must be333 μm. If an illumination fiber is used, then the illumination NA mustbe approximately 0.22.

Clearly more than two radiation sources (with different wavelengths) maybe used at a time.

FIG. 7 shows an example of a wavelength demultiplexer in the detectionbranch. For simplicity, the separation of only two wavelengths is againshown. The demultiplexer is similar to the muliplexer, except that thegrating is placed in the pupil plane and not in the object plane. Thelight that is diffracted by the grating in the Littrow mounted grating16 is transmitted by the lens L2, which makes two object images withwavelengths λ1 and λ2 in the object plane. This plane may contain fieldstops with n holes (n=2 in this case), which should be sufficiently wideto avoid spatial filtering to avoid disturbing the spectrum. Each holeof the field stop 40 also has a wedge 62 with a unique wedge angle. Thiswedge 62 ensures that the angle-resolved scatter spectrum for eachwavelength is imaged on a different part of the CCD detector 32. The CCDdetector is based at the second pupil plane 40.

Since the wedges 62 can deflect the light in two directions, it ispossible to realize an efficient filling of a CCD detector with manyangle-resolved spectra.

In order to obtain reproducible results, the targets should be wellfocused. In order to achieve this, the pupil plane 40 of a high NAobjective is imaged on a detector with a double telecentric system asshown in FIG. 8 according to an embodiment of the invention. In allembodiments, the NA is high, desirably at least 0.9.

A knife edge 70 in the intermediate object plane 42 blocks one half ofthe intermediate object image. The edge may be a Foucault knife-edge.

The knife-edge helps to focus the image of the radiation onto thesubstrate. For each orientation, the intensity in the outer regions (orpractically speaking, in two halves) of the pupil plane 40 is sampled.In the case of a defocus, a difference in intensities I1 and I2 isproduced. Focus F is given as:

$\begin{matrix}{F = {k\frac{{I1} - {I2}}{{I1} + {I2}}}} & (23)\end{matrix}$

The proportionality factor k is independent of the image and needs to bedetermined only once, though since the focus sensor can be used in anintegrating feedback loop, the precise value of k is not important.

Illumination sources are not always homogeneous and must be calibratedand corrected for in order to guarantee precise exposure of a substrate.Inhomogeneity may be caused by the illumination sources themselves, orby the roughness of a surface coating of one or more reflectors in theillumination path. Normalization of the illumination beam may be doneusing an aluminum mirror. However, this normalization may fail when theobject to be measured (i.e., a grating or the substrate) generateshigher diffraction orders. These cause tool induced shift errors inoverlay applications.

In an embodiment, therefore, the scatterometry system further comprisesone or more mirrors in the illumination beam. More specifically, the oneor more mirrors may be a fiducial on the substrate table and may be madeof aluminum. The one or more mirrors either tilt or exist at differenttilt angles in order to create at least two images reflected atdifferent angles. For each tilt angle, the detected spectrum shifts inthe same direction as the direction of the tilt. These images aredetected and combined into a differential equation, from which theillumination profile of the radiation beam may be determined. Theresultant illumination profile is used to correct measurements of theproperty of the reflected spectrum at higher diffraction orders.

The measured signal, M0(k), is represented as:M ₀(k)=[A(−k)R ₀(k)+A(−k±k _(G))R _(∓1)(x)+ . . . +A(−k±Nk _(G))R_(∓N)(x)]B(k)   (24)where:

-   -   A(k) is the unknown illumination intensity at position k in the        pupil plane;    -   B(k) is the unknown optical loss in the detection branch of the        sensor; and    -   R_(±N) is the diffraction efficiency of the N^(th) order of the        grating object.

In practice, the illumination intensity varies because of a slowlyvarying inhomogeneous illumination beam and surface roughness of theoptics and coatings in the illumination path. The surface roughness ofan optical coating generally gives rise to a grainy appearance of theillumination beam in the pupil plane.

A reference measurement may be carried out on a highly reflectingaluminum mirror, which yields the following measured signal:M _(M)(k)=A(−k)R _(M)(k)B(k)  (25)

Normalizing the measurement of the object with the reference yields:

$\begin{matrix}{\frac{M_{0}(k)}{M_{M}(k)} = {\frac{R_{0}(k)}{R_{M}(k)} + {\frac{A\left( {{- k} \pm k_{G}} \right)}{A\left( {- k} \right)}\frac{R_{\mp 1}(x)}{R_{M}(k)}} + \text{…} + {\frac{A\left( {{- k} \pm {Nk_{G}}} \right)}{A\left( {- k} \right)}\frac{R_{\mp N}(x)}{R_{M}(k)}}}} & (26)\end{matrix}$

It can be seen that the losses in the detection branch are eliminated bythis normalization.

However, inhomogeneities in the illumination are only eliminated for thezero diffraction order (i.e. the specular reflection). Higherdiffraction orders retain an unknown error term of the form:

$\begin{matrix}\frac{A\left( {{- k} \pm {Nk_{G}}} \right)}{A\left( {- k} \right)} & (27)\end{matrix}$

In order to eliminate this term, the illumination profile A(k) should becalibrated as discussed below.

The mirror may be a single convex or concave mirror (e.g., mirrors 52 bor 52 a, respectively, shown in FIGS. 15B and 15A, respectively), or itmay be a plane mirror that is actively tilted over a range of anglesduring detection. Alternatively, there may be a range of mirrors (e.g.,element 52 c shown in FIG. 15C) at different tilt angles. The measuredreflection angle may be in a radial direction (this alters the magnitudeof the tilt) or in an azimuthal direction (this alters the direction ofthe tilt).

The method used to determine the differential equation will now bedescribed in 1-dimension. The extension to 2 dimensions is trivial.

A reference mirror is measured for two small opposite mirror tilts±θ_(M) of the order of 1 mrad. As a result of this tilt, the measuredpupil image will shift. Two slightly shifted images are thereforemeasured:M _(±θ)(k)=A(−k±Δ(k))R _(M)(k)B(k)C(k;±θ)  (28)

Here, Δ is the shift in the pupil plane, which generally depends on theposition k in the pupil plane. For an aplanatic system:Δ(k)=2θ_(M)√{square root over (1−k ²)}  (29)

C in equation (28) accounts for the redistribution of the reflectedintensity and for an aplanatic system:

$\begin{matrix}{{C\left( {k;\Delta} \right)} = {1 + \frac{2\theta_{M}k}{\sqrt{1 - k^{2}}}}} & (30) \\{{Q_{M}(k)} = \frac{M_{+ \theta} - M_{- \theta}}{M_{+ \theta} + M_{- \theta}}} & (31)\end{matrix}$where M_(+θ) and M_(−θ) are spectra measured at a small positive tiltand small negative tilt respectively.

Here, the subscript ‘M’ of Q is used to emphasize that it concernsmeasured data. For small tilts, an approximation may be:

$\begin{matrix}{{A\left( {k + {\Delta(k)}} \right)} \cong {{A(k)} + {\frac{dA}{dk}{\Delta(k)}}}} & (32)\end{matrix}$

Using this linearization yields for Q the differential equation:

$\begin{matrix}{\frac{Q(k)}{\Delta(k)} = {\frac{1}{A(k)}\frac{dA}{dk}}} & (33)\end{matrix}$

This equation is easily solved to yield:

$\begin{matrix}{{A(k)} = {\exp\left\lbrack {\int\limits_{0}^{k}{\frac{Q\left( k^{\prime} \right)}{\Delta\left( k^{\prime} \right)}{dk}^{\prime}}} \right\rbrack}} & (34)\end{matrix}$

The above derivation can be easily extended to 2 dimensions. Inpractice, the measured data is not continuous but is digitized sampleddata. However, this does not alter the concept derived above.

In practice, a plane mirror (e.g., element 52 shown in FIG. 5 ) may beemployed that is mechanically tilted using actuators (e.g., actuator 51shown in FIG. 5 ). A more elegant and simple approach is the use of aconcave or convex mirror (e.g., elements 52 a and 52 b, respectively,shown in FIGS. 15A and 15B, respectively) with a radius of curvature Rand lateral position x. The local height z of a curved mirror isdescribed by:

$\begin{matrix}{z = \frac{x^{2}}{2R}} & (35)\end{matrix}$

The local slope of the surface θ scales linearly with the lateralposition x:

$\begin{matrix}\begin{matrix}{\theta \cong \frac{dz}{dx}} \\{= \frac{x}{R}}\end{matrix} & (36)\end{matrix}$A concave or convex spherical aluminum fiducial on the substrate stagetherefore renders the calibration straightforward because the propertilt is simply achieved by moving the fiducial to the proper locationunder the detector.

An embodiment of the invention uses a radiation beam with an annularintensity distribution in a conjugate plane to the substrate. In orderto create the annular intensity distribution, the radiation source maycomprise mechanical blades, spatial light modulators or spatiallycoherent broadband lasers and a zoom-axicon (i.e. to create a ring oflaser light). In an embodiment, the annular radiation beam comprisessmall-Φ illumination.

Implementing annular radiation has advantages over, say, inserting ablade, because there is no radiation loss because almost all the photonsare “used”. This is particularly important where radiation sources suchas UV or DUV are used because they emit fewer photons than more abundantradiation sources and so losing a number of those photons is morenoticeable. In particular, this is noticeable in signal collectionbecause the lithographic tool suffers a certain amount of delay if thereis a lower radiation intensity. Annular radiation sources have a furtheradvantage of not causing internal reflections as blades might. Internalreflections require blocking to avoid radiation artifacts. Of course,other illumination techniques, such as quadrupole illumination, whichoffer one or more of the same advantages may be used.

Ideally, the annulus of the annular radiation is placed in the pupilplane of the high NA lens. However, the pupil plane is not directlyaccessible and in practice, the annulus is placed in a back-projectedimage of the pupil plane in the illumination branch of thescatterometer. An advantage of annular illumination is that theintensity of the +1/−1 diffraction order of a grating with a small pitchof the order of λ/NA may be separately measured.

This embodiment may be used for calculating variations in substrate tiltby putting a shaped obscuration in the radiation beam and detectingchanges in the width and shape of the shaped obscuration on thesubstrate caused by variations in the substrate tilt. The shapedobscuration may be, for example, a cross-hair as shown in FIGS. 9 a and9 b . It may, of course, be any other shape and it does not have to bein the center of the pupil plane.

The idea of measuring substrate tilt is based on the fundamentalrelation that a tilt in the substrate plane causes a shift in the pupilplane. In the present embodiment, a cross-haired obscuration is placedin the center of the illumination beam. This produces a black cross-hairin the scattered light in the pupil plane as shown in FIG. 9 a.

The location of this cross will vary if the substrate tilt changes. As aresult, the difference may be measured between this pattern (at zerotilt) and an actual measurement at an unknown tilt to obtain an image asshown in FIG. 9 b . A small tilt in the substrate does not lead to asubstantial shape change in the annulus of radiation, but rather, itwill lead to a shift of the pupil plane image. This shift is generallysmall and of the order of 0.1 pixels. In order to be able to detect sucha small shift, the values between pixels may be interpolated by curvefitting, for example. By fitting a curve through the dark-lighttransition that occurs at the edge of the annulus, sub-pixeldisplacements of the annulus may be measured.

The width and sign of these transitions can be used to calculate andcorrect for the substrate tilt in 2 dimensions. In this way thesubstrate can be measured at constant (zero) tilt.

FIG. 10 shows the diffraction orders of small pitched gratings detectedusing radiation with an annular intensity distribution in a conjugateplane to the substrate. Using an annular intensity distribution allowsthe shape of the images as shown in FIG. 10 and thereby allows clearerand more precise measurement of substrate tilt. The image labelled 0 isthe central zero-order diffraction order as imaged in the detector. Theimages labelled −2, −1, 1 and 2 are higher diffraction orders. Thesehigher diffraction orders are shifted with respect to the lowerdiffraction order and so are easier to measure for overlay metrology ofisolated 1-D and 2-D features.

In order to speed up calculation times, there are cases in which it maynot be necessary to calculate a simulated signal in every singleposition in the pupil plane, especially when smooth variations areexpected. In these cases, a coarse grid may be measured and a pixelinterpolation technique used to interpolate the overall shape at thepupil plane. An annular beam is more advantageous in this case, too,because there are areas in the pupil plane that only receive radiationfrom first order diffraction. If a block beam were used, for instance,each point in the pupil plane would receive radiation from either thezeroth order or a combination of the zeroth order and the first order,causing errors in the measurement at the pupil plane.

Normal measurements using a scatterometer involve measuring the one ormore properties of a single target on a single substrate with a singlepolarization at one time. This may limit the throughput of substratesthrough the scatterometer, and potentially exposure steps. An embodimentof the invention uses an illumination source to project a plurality ofillumination spots onto a substrate. The detector of the scatterometersimultaneously detects an angle-resolved spectrum of the plurality ofillumination spots reflected from a surface of the substrate. Theplurality of illumination spots may be created using a doubleillumination fiber or a Wollaston prism to create two orthogonallypolarized illumination spots.

FIG. 11 shows part of the scatterometer hardware. Two illumination spots70 are split in beam splitter 50 before being transmitted down throughthe high numerical aperture objective positioned in the pupil plane 40onto the substrate 6. The reflected beam is transmitted upwards throughtwo wedges 62 that separate the two angle-resolved spectra in the pupilplane, the wedges themselves being positioned in the intermediate imageplane 42. The illumination beams are then detected by the CCD on there-imaged pupil plane 40 at the top of FIG. 11 . Two, or even more,parallel measurements may thereby be made—for example, of horizontal andvertical lines for a single polarization or even for both horizontal andvertical lines for both TE and TM polarization.

An embodiment of the invention converts the scatterometer into anellipsometer. In order to do this, the illumination branch furtherincludes a first polarizer configured to linearly polarize the radiationbeam; a beam splitter configured to split the radiation beam into twoorthogonal components (ETE, ETH); a second polarizer configured topolarize the scattered beam; a variable compensator (a Pockells Cell,Wollaston prism pair or Soleil-Babinet compensator) positioned betweenthe first and second polarizers, the variable compensator beingconfigured to vary the optical path difference between orthogonallypolarized components (and optionally between the beam splitter and thehigh numerical aperture lens); and a 2-dimensional detector fordetecting sinusoidal intensity variation of the resultant beamcomponents. The compensator is most commonly in the main illuminationbranch of the scatterometer, though it may of course be in a secondillumination branch. The 2-dimensional detector, such as a ComplementaryMetal Oxide Semiconductor detector (CMOS), has a high frame rate, i.e.in the region of 1000 frames per second.

FIG. 12 shows how the angular-resolved spectroscopic concept is turnedinto an angle-resolved spectroscopic ellipsometer. An illumination beamwith two wavelengths, λ1 and λ2 is transmitted through a 45° polarizer72, reflected off the substrate 6 and transmitted through a variablecompensator 74 before being polarized again by a 45° polarizer 75.Between the beam splitter 73 and the variable compensator 74, theillumination beam is divided into two beams with a phase difference Δbetween the TE and TM polarized beams. The grid 36 in FIG. 12 shows the2-D detector array and the time-dependent intensity variation in onepixel of this array. The other pixels will show a comparable variation.The beams are passed through two bandpass filters 76 to obtain theillumination profiles of λ1 and λ2. The resultant ellipsometricparameters cos(Δ), sin(Δ) and tan(Ψ) are virtually insensitive tointernal sensor scattering and so the signal to noise ratio can beimproved. The operation is modeled with Jones vectors and matricesbelow, though it could also be modeled using Mueller matrices, whichenable the inclusion of imperfections of the optical components in themathematical models.

The illumination field after the first polarizer is 45° polarized anddescribed by the Jones vector:

$\begin{matrix}{E_{inc} = \begin{bmatrix}1 \\1\end{bmatrix}} & (37)\end{matrix}$

Basis vectors correspond to TE and TM polarized radiation that isincident on a target on a sample. The act of reflecting off the samplecauses an alteration in the amplitude and the phase of the scattered TEand TM components. This can be represented by a Jones matrix:

$\begin{matrix}{J_{sample} = \begin{bmatrix}R_{TE} & 0 \\0 & {R_{TM}e^{j\Delta}}\end{bmatrix}} & (38)\end{matrix}$where Δ is the phase difference between the TE and TM components of thescattered fields and R_(TE) and R_(TM) are the amplitudes of,respectively, the scattered TE and TM fields.

These parameters are a function of angle of incidence and wavelength.Ignoring any phase and amplitude variations introduced by the high-NAlens and the beam splitter, for the incident field on the compensator:

$\begin{matrix}\begin{matrix}{E_{c\;\_\; i\mspace{11mu} n} = {J_{sample}E_{inc}}} \\{= \begin{bmatrix}R_{TE} \\{R_{TM}e^{j\Delta}}\end{bmatrix}}\end{matrix} & (39)\end{matrix}$

The compensator introduces a time-varying optical path difference (OPD)variation between the TE and TM components. If the wavelength of theradiation is λ, for the Jones matrix of the compensator:

$\begin{matrix}{J_{comp} = \begin{bmatrix}1 & 0 \\0 & e^{j\; 2\;\pi\frac{{OPD}{(t)}}{\lambda}}\end{bmatrix}} & (40)\end{matrix}$and so the field after the compensator is:

$\begin{matrix}\begin{matrix}{E_{c\;\_\;{out}} = {J_{comp}E_{c\;\_\; i\; n}}} \\{= \begin{bmatrix}R_{TE} \\{R_{TM}e^{j{({\Delta + {2\;\pi\frac{{OPD}{(t)}}{\lambda}}})}}}\end{bmatrix}}\end{matrix} & (41)\end{matrix}$

The second polarizer is oriented at 45° and has a Jones matrix:

$\begin{matrix}{J_{pol} = {\frac{1}{2}\begin{bmatrix}1 & 1 \\1 & 1\end{bmatrix}}} & (42)\end{matrix}$and so the field after the second polarizer is:

$\begin{matrix}\begin{matrix}{E_{{pol}\;\_\;{out}} = {J_{pol}E_{c\;\_\;{out}}}} \\{= {\frac{1}{2}\begin{bmatrix}{R_{TE} + {R_{TM}e^{j{({\Delta + {2\;\pi\frac{{OPD}{(t)}}{\lambda}}})}}}} \\{R_{TE} + {R_{TM}e^{j{({\Delta + {2\;\pi\frac{{OPD}{(t)}}{\lambda}}})}}}}\end{bmatrix}}}\end{matrix} & (43)\end{matrix}$

The intensity incident on the detector array is:

$\begin{matrix}\begin{matrix}{I_{d} = {E_{{pol}\;\_\;{out}}^{T} \cdot E_{{pol}\;\_\;{out}}^{*}}} \\{= {\frac{1}{2}\left\lbrack {R_{TE}^{2} + R_{TM}^{2} + {2R_{TE}R_{TM}{\cos\left( {\Delta + {2\pi\frac{OP{D(t)}}{\lambda}}} \right)}}} \right\rbrack}}\end{matrix} & (44)\end{matrix}$

If the OPD increases linearly over the measurement time interval, OPD=Kt

This yields a time-harmonic intensity variation:

$\begin{matrix}{I_{d} = {\frac{1}{2}\left\lbrack {R_{TE}^{2} + R_{TM}^{2} + {2R_{TE}R_{TM}{\cos\left( {\Delta + {\Omega t}} \right)}}} \right\rbrack}} & (45) \\{{{where}\mspace{14mu}\Omega} = {2\pi\frac{K}{\lambda}}} & (46)\end{matrix}$

The contrast of the intensity variation is directly related to theellipsometric parameter tan(Ψ) and the phase of the sinusoidal variationdirectly yields the ellipsometric parameters cos(Δ) and sin(Δ). In astandard ellipsometric scatterometer, tan(Ψ) and cos(Δ) are the signalsthat are measured and simulated to obtain the profile information. Inthat case, tan(Ψ) and cos(Δ) are recorded as a function of wavelength.In an embodiment of the present invention, tan(Ψ) and cos(Δ) areobtained as a function of position in the pupil plane and can be usedfor similar analyses. In particular, the ellipsometric parameters areused to measure layer thickness by solving an inverse scatteringproblem, i.e. the measured parameters are compared with modeledparameters and the stack parameters are determined by minimizing theroot-mean-square difference (or any other suitable metric) between themeasured and modeled parameters.

Because the frequency of the variation depends on the wavelength, thevarious wavelengths can be separated with a bandpass filter. This can beeasily realized via signal processing with, for example, discreteFourier Transform techniques.

The compensator may also be placed in the illumination branch. Moreover,it may also be placed between the beam splitter and a high numericalaperture objective. This has the advantage that the OPD variation isdoubled.

The 2-D detector is a significant aspect of this concept—to ensuresufficiently short measurement times, it should have a high frame rate.CMOS detectors can achieve very high frame rates, for example 1000frames per second.

Measuring overlay as described starting at paragraph 52 above may notallow for the measurement of large overlay, in particular, overlay equalto an integer times the grating pitch. Clearly, the ability to detectoverlay smaller than the grating pitch is of no use if there is anoverlay where the grating lines are lined up with each other, butshifted by several grating pitch widths.

An embodiment of the invention therefore uses a second detector branchalready present in the scatterometer (and discussed above) to carry outcoarse overlay measurements to determine whether coarse errors exist,such as whether the grating overlay is in fact greater than the pitch ofthe grating. A coarse overlay measurement is an imaging-based technique,wherein a second camera looks at an image of two overlapping gratingsand determines whether there are large displacements by comparing thepositions of the edges of markers on a substrate. A perfect overlay willhave perfectly aligned marker edges. Pattern recognition algorithms areused to determine the edge of a grating in the process layer and theedge of the grating in the resist layer. This measurement is done on thefour sides or corners of a grating pair. The measured edge positions areused to calculate the position of the resist grating relative to theposition of the grating in the process layer.

The fact that scatterometry on its own cannot measure overlay that isequal to a multiple number of the grating pitch is a fundamentallimitation because the measurement principle is based on gratingcoupling that varies periodically with the grating pitch. In otherwords, zero overlay and an overlay equal to the pitch yield identicalresults.

The scatterometer according to an embodiment of the present inventionprovides a very simple solution. The scatterometer comprises a separateimaging branch that images the substrate surface on a CCD camera. Thissecond camera branch is used to measure the position of the substratethrough an alignment and pattern recognition step. The second branch isshown schematically in FIG. 13 .

The pupil plane 40 measurement (the actual angle-resolved measurement)requires an illumination source that underfills the target at the objectplane 42 (i.e. the measurement spot is smaller than the measurementtarget). The pupil plane imaging illumination beams are shown as solidlines in FIG. 13 . In this case, only a portion of the target ismeasured and structures outside the target area are not illuminated. Ifthe measurement spot fills or overfills the measurement target, themeasurement signal is disturbed by the area surrounding the target anddata interpretation and signal analysis are unnecessarily complicated.

The image plane measurement, on the other hand, must overfill the targetin order to detect the alignment because the complete pupil plane mustbe sampled, including the contours of the target. The rays for the imageplane measurements are shown as dashed lines. The image of the objectplane is formed on a first CCD camera 80 and the image of the pupilplane is formed on a second CCD camera 82.

FIG. 14 shows one possible example of an overlay target for zero overlay(left-hand drawing) and an X-overlay equal to twice the grating pitch(right-hand drawing). The pupil plane measurement would yield the samemeasured overlay of zero for both situations making it an unreliablemeasurement. The image plane measurement, however, can clearlydistinguish between these two situations. In this way, a robusttwo-stage metrology scheme may be carried out as follows:

(1) Two image plane measurements are carried out to verify that there isno large overlay present.

(2) If the previous measurement indicates that overlay is less thanapproximately 200 nm, the pupil plane measurements are carried out.

The 200 nm criterion is an indicative example. It may be made to anysensible threshold. Assuming that the image plane CCD has 1000×1000pixels and assuming a pixel pitch of 100 nm at substrate level, thetotal field of view will be 100×100 μm², which is adequate for patternrecognition and alignment while still allowing coarse overlaymeasurements with an accuracy of the order of 20-50 nm.

Coarse overlay can only be measured when the entire alignment marker isvisible to the CCD. If, for example, only the center part of the markeris visible, the substrate table needs to be moved to the edge of themarker to enable the measurement of the coarse overlay. This calls foradditional movement of the table, thereby slowing the measurement takingprocess. A larger field of view allows the capture of the marker in one“stroke” and a coarse measurement to be carried out quickly while asecond camera is free to capture the image on the pupil plane and obtainthe detailed overlay information.

The field of view for capturing the relevant image can be reduced evenfurther if the results of edge pre-alignment and coarse substrate alignin the exposure tool are used. With these data, it is possible topredict the location of the markers on the substrate with μm accuracyafter the edge pre-alignment in the overlay metrology module iscomplete.

An embodiment of the invention detects not just overlay, but may detectdamaged gratings using a scatterometer arranged for CD metrology ongratings or other periodic structures. The scatterometer normallydetects specular radiation, i.e. lowest order radiation that has beenreflected directly off the grating. Local distortions in the gratingdestroy the periodicity of the grating and result in scattering in anon-specular direction. The scatterometer can be used to detect anangle-resolved spectrum of the scattered beam at various angles outsideits specular direction. Radiation with an annular intensitydistribution, or small-Φ illumination, may be used for greater accuracyand images that easier to read.

An embodiment of the invention may be used to detect bubble defects inan immersion lithographic apparatus, where a liquid is introducedbetween the projection system and the substrate as discussed above.Previously, bubble defects have been measured using an off-line defectinspection tool. Off-line tools take a longer time to produce resultsthan on-line tools because substrates must be taken out of theproduction line and queued. Bubbles in the liquid cause a surfaceimperfection on the substrate, which will cause radiation scatteringwhen the surface is exposed to radiation. This scattered radiation ismeasured using a scatterometer according to an embodiment of theinvention and the cause of the scattering may be extrapolated back tobubble defects.

While specific embodiments of the invention have been described above,it will be appreciated that the invention may be practiced otherwisethan as described. The description is not intended to limit theinvention. The specifically described embodiments are extensions to ageneral operating principle and are not necessarily mutually exclusive;they are all combinable in a single metrology tool to increase itseffectiveness based on results seen at a detector as described above.Further, although the embodiments described herein relate to lithographyapplications, the hardware and applications are not limited to these.They may be used for other applications such as monitoring etch processsteps and the like.

The invention claimed is:
 1. A method, comprising: using a liquid in aspace between a substrate and a lens; directing, using the lens, aradiation beam from a radiation source toward a pattern formed on thesubstrate; and measuring asymmetries between intensities ofcorresponding diffraction orders in an angle-resolved spectrum of aradiation beam diffracted from the pattern at a plurality of angles anda plurality of wavelengths substantially simultaneously to measure aproperty of the substrate.
 2. The method of claim 1, wherein themeasuring asymmetries comprises measuring at least one of: an intensityof a transverse magnetic and a transverse electric polarized light, anda phase difference between the transverse magnetic and the transverseelectric polarized light.
 3. The method of claim 1, further comprising:coupling off a portion of the radiation beam emitted from a radiationsource for a separate measurement.
 4. A method, comprising: placing awavelength multiplexer between a radiation source and a substrate;placing a wavelength demultiplexer between the substrate and a detectorlocated in a pupil plane of a high numerical aperture lens; using aliquid in a space between the substrate and the high numerical aperturelens; directing, using the high numerical aperture, a radiation beamfrom the radiation source toward the substrate; and measuring, using thedetector, an asymmetry in an angle-resolved spectrum of a radiation beamreflected from a surface of the substrate at a plurality of angles and aplurality of wavelengths substantially simultaneously to measure aproperty of the substrate.